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lubasha [3.4K]
3 years ago
12

In Euclidean geometry, the sum of the measures of the interior angles of a pentagon is 540°. Predict how the sum of the measures

of the interior angles of a pentagon would be different in spherical geometry.
A.
The sum would be greater than 540°.
B.
The sum would still be 540°.
C.
The sum would be less than 540°.
D.
The sum would less than or greater than, but never equal to, 540°.
Mathematics
1 answer:
Blizzard [7]3 years ago
6 0
In Euclidean geometry, the sum of the measures of the interior anlges of a pentagon is 540°. 

The sum of the measures of the interior angles of a pentagon would be different in spherical geometry because A.) THE SUM WOULD BE GREATER THAN 540°
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Each of six jars contains the same number of candies. Alice moves half of the candies from the first jar to the second jar. Then
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Answer:

The number of candies in the sixth jar is 42.

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⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:

\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x

⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:

\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x

⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:

\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x

⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:

\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x

Now, it is provided that at the end, 30 candies are in the fourth jar.

Compute the value of <em>x</em> as follows:

\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}

Compute the number of candies in the sixth jar as follows:

\text{Number of candies in the 6th jar}=\frac{63}{32}x\\

                                                    =\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42

Thus, the number of candies in the sixth jar is 42.

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